A Game-Theoretic Approach for Electric Power Distribution during Power Shortage: A Case Study in Pakistan

Power supply is the cornerstone for the sustainable socio-economic development of any country. In a developing country like Pakistan, shortage of power supply is the main obstacle to its economic growth, making it a disputed and contested resource among different administrative units/provinces and socio-economic sectors. A key challenge is allocating the limited available power among provinces with conflicting and competing needs amid the supply-demand gap. In this research, the allocation of energy during a shortage is considered as a game-theoretic bankruptcy problem. Five bankruptcy rules namely the Proportional Rule, Constraint Equal Award Rule, Constraint Equal Loss Rule, Talmud Rule and Piniles Rule are used for power allocation among the provinces of Pakistan. Each province is characterized by its power demand. A new framework is also proposed for power allocation, which synthesizes the Nash bargaining solution concept with bankruptcy theory to resolve power-related disputes among the four provinces within Pakistan. Additionally, a new method is introduced in this study to compare and contrast the different allocation rules. The results suggest that the basic power demands of the provinces can be satisfied by the proposed disagreement points among the provinces, and the bargaining weights can highlight the role of different levels of power claims, lengths of transmission lines, and variations in population among provinces. The findings also suggest that, due to the lowest dispersion, the proportionate rule is the most suitable method for power allocation among the provinces. The paper combines relevant bankruptcy rules with Nash bargaining theory to propose an algorithm for addressing power sector supply-demand mismatches in Pakistan.